The prior art is replete with various optical fiber structures. One is a plastic clad fiber having a cross section shown in FIG. 1 in which reference numeral 1 designates a core and 2 a clad or sheath portion made of resin containing fluorine or silicon. FIG. 2 shows a refractive index distribution of the section of the optical fiber in FIG. 1. Refractive indexes of the core 1 and the clad or sheath 2 are n.sub.1 and n.sub.2, respectively. The relation of n.sub.1 &gt;n.sub.2 is established and almost all of the optical energy within the fiber is transmitted through the core 1. In connecting such optical fibers, there are various factors detriorating the optical transmission efficiency. The primary factor is radial displacement of the optical axes of the fibers in connecting thereto. Many methods of connecting the optical fibers with a high transmission efficiency has been heretofore proposed. In these methods, the outer peripheral surface of the clad 2 is utilized as a fundamental or base to utilize the optical fibers. For this reason, if the core is eccentrically disposed in the clad 2 or the thickness of the clad 2 is nonuniform, the cores are displaced as shown in FIGS. 3 and 4. As the result, the optical transmission efficiency is greatly reduced around the connecting portion.